Public engagement, storytelling and complexity in maths communication

(1)

Dipartimento di Scienze Pure e Applicate

Corso di Dottorato: Scienze di Base e Applicazioni

Curriculum Scienze della Complessità – ciclo XXX

Ph.D. Thesis

Public Engagement, Storytelling and

Complexity in Maths Communication

Supervisor

Prof. Gian Italo Bischi

Candidate

Prof. Andrea Capozucca

Dottorato in Scienze della Complessità

Ciclo XXX – A.A. 2016/2017

(2)

To Francesca who made all of this possible

(3)

iii

List of figures

Figure 2.1 Prof Chris Budd in his office

Figure 2.2 The cartoon with the British “champions” of the communication of mathematics (in the foreground, from the left, Zeeman, Stewart and Du Sautoy can be recognized) on a wall of Prof Budd’s office

Figure 2.3 Prof Budd’s cartoon

Figure 2.4 From the left Prof Budd, Andrew Ross and Andrea Capozucca

Figure 2.5 Margarida Dolan, who teaches science communication and public engagement to undergraduates and graduates, with one of her student

Figure 2.6 The pub The Raven in Bath

Figure 2.7 Prof Budd is honoured with OBE at Windsor Castle (from the left Sue, Prof Budd’s wife, Prof Budd, his daughter Bryony and his mother Jillian)

Figure 2.8 The Department of Engineering’s stand about electricity at the School Science Fair within Bath Taps into Science

Figure 2.9 The Department of Biology’s stand at the School Science Fair within Bath Taps into Science

Figure 2.10 The Royal Casino organized by the Mathematics Communication Group at the School Science Fair within Bath Taps into Science

Figure 2.11 A general view on some of the stands at the School Science Fair within Bath Taps into Science

Figure 2.12 Stands full of visitors in the central pavillon at the Family Science Fair Figure 2.13 The stand of the Department of Natural Science at the Family Science Fair

Figure 2.14 The audience waiting for the beginning of Andrew Ross’s “chemistry show” at the Family Science Fair

Figure 2.15 Gracelands Café: outside

Figure 2.16 Alex Bellos at Gracelands Café during the interview Figure 2.17 Alex in India interviewing the head of Vedic maths Figure 2.18 Giving a talk at the Glastonbury Festival

Figure 2.19 Alex and his elliptical pool table

Figure 2.20 A book launch in Brazil for Alex’s Adventures in Numberland

Figure 2.21 A prize ceremony (best non-fiction book at the British book awards for Alex’s Adventures in Numberland)

Figure 2.22 Andrew Jeffrey with some students at the end of a show Figure 2.23 Andrew Jeffrey during a magic show

Figure 2.24 Andrew Jeffrey during the 2007 award ceremony of the Sussex Magic Circle Competition

Figure 2.25 Two images from Andrew Jeffrey's Magic of Maths! Show Figure 3.1 Public Engagement Triangle

(6)

vi

start by placing a particular topic or their research in a historical context, the public wants to know the key point at the start. Photo from

https://www.aaas.org/page/communicating-engage

Figure 4.2 Visitors and me struggling with the Soap Bubble Wires at the IMA Stand, Big Bang Fair Birmingham

Figure 4.3 From left to right: Andrea Capozucca, Silvia Benvenuti, Agata A. Timón Garcia-Longoria, Janine McIntosh, Costanza Rojas-Molina, Hyungju Park, Andreas Daniel Matt, Jean-Paul Truc and Gang Liu

Figure 4.4 Cedric Villani and me

Figure 4.5 Photos from VereMath Exhibit Figure 4.6 Photos from VereMath Walk

Figure 4.7 Photos from VereMath Busking Show Figure 4.8 Photos during the laboratories

Figure 4.9 The advertise of the event “Caffè Scienza”

Figure 4.10 Photos from two different Science Cafes held in Sant’Elpidio a Mare, Montegranaro and Fermo

Figure 5.1 The cover of the book

Figure 5.2 Barbara and I before the book launch at the University of Camerino Figure 6.1 Sketches for pendulum cross-sectional exhibit

Figure 6.2 Sketches for choreography with mirrors

(7)

vii

List of tables

Table 3.1 Adapted from Bultitude K. (2010), Presenting Science. In: Brake M.L., Weitkamp E. (eds.), Introducing Science Communication. London, Palgrave MacMillan

Table 4.1 First syllabus draft Table 5.1 Results of the survey

(8)

viii

Acknowledgements

6 April 2014. Saturday. A spring sunny day in Orvieto. After a pleasant lunch, I and my colleague Stefano Leonesi decided to take two hours off from the conference program to visit the wonders of the city. Waiting in line for a guided tour to visit the underground Orvieto, we started talking about mathematics. Pretty soon, our conversation turned to other issues. I told Stefano the vicissitudes that prevented me from continuing my studies after graduation addressing me towards teaching. Stefano looked at me and said: “A few days ago, a colleague of the University of Urbino told me that in the next few months there will be a call for two PhD posts in Science of Complexity. I really think you should try. Why don’t you?”

This is how it all began. And now I’m here, three years later, to write my acknowledgements at the end of this doctorate. Embarking on a doctorate course at 40, it was a disruptive, challenging and inspiring experience that required me to put myself out there and rearranged my life. So, my first thanks goes to Stefano Leonesi who planted a bug in my ear when everything seemed well-established, scientifically speaking.

Then, many thanks are due to my Supervisor Prof. Gian Italo Bischi for his wisdom, knowledge, expertise, passion, willingness and careful thoughts. He stood by me with patience and care, I dare say fatherly in his manner, leaving me the freedom to choose and the capacity to continuously improve my knowledge and skills. During our fruitful discussions, I learned the pleasure of looking at things with intellectual curiosity taking care of all the possible connections with other bodies of knowledge. In short, it wouldn’t be enough twice the pages of this thesis to give back all I received from him. I hope to continue our inspiring cooperation in the future.

This thesis was conceived, rooted and expanded by the guidance and questioning of several individuals, all of whom have offered valuable insights and inquiries along the way. First and foremost, I would like to thank Prof. Vincenzo Fano, the Coordinator of the PhD program in Science of Complexity, for his valuable suggestions to improve this research work. I’d also like to thank Unicam Science Outreach members, in particular Silvia Benvenuti, Mario Compiani and Alessandra Renieri. Their guidance, questioning and collaboration were so precious to tackle the complex science and maths communication matters. A sincere thanks goes to Mauro Comoglio who was, is and will be a helpful and inspiring point of reference in the world of education always open to dialogue and debate.

A special thank you to Marco Fermani who believed and fully involved himself in FOTCAB project from the very beginning. His background in physics coupled with his expertise in music composition and playing were a huge support to implement and develop the project. The time spent together has always been inspiring for me. Thanks to Simone Giorgini for his musical arrangements

(9)

ix

and recording of “Logistic Map Song”. A huge thanks to Diego Zallocco for creating “Music2Chaos” sonification program. And particular thanks go to Valentina Di Sante and Silvia Gambini for their creative collaboration in the dance part of the project and for their choreography of “Logistic Map Song” presented during Bridges 2016 workshop.

Then, I would like to thank Chris Budd, Kristof Fenyvesi and Erik Stern for having me during my visiting periods abroad. Above all, for their valuable communication tips, their essential and important support in the development of the theoretical structure of my research and in the design exploitation phase of the engagement and outreach activities we set up.

Many thanks to all my friends on who I was always able to count over these three years through times of happiness and times of sadness. Guys, you’re great.

Last, but certainly not least, thank you to my family for always supporting me in my endeavors. So, thank you Dad for being there quietly. Sincere thanks to Franco and Maria for their concrete support. Thank you Sebastiano for being simply “Maccio” and cause of great joy along the path. Thank you Silvia for putting up with a “father in computer” especially over the past year. Your smiles and hugs are the greatest gift of all, much more than everything I will ever able to write. A very special thanks to my wife, Francesca, without whom none of this would have been possible. I actually appreciate your sacrife, your love and your devotion. You forced me to try, supported me and believed in me more than I did. Even my most absurd explorations were conceivable in your eyes. And I owe this all to you.

And finally, thanks to my Mother who always follows and protects every step I take in every single moment of my life.

(10)

Chapter 1 Introduction

All over the globe, every day of the week, mathematicians are carrying out research, providing new theorems, inventing new definitions, solving problems, posing new ones. They create a language and new models which become instruments for a deeper understanding of scientific, economic and social complexities. The vast majority of the public have no idea that any of this is happening.

It’s part of the researchers’ mission to raise the general public awareness of mathematics and science in general. This need is further emphasized by a survey of Eurobarometer 20101: the society is strongly interested in science but, at the same time, is often scared by the risks posed by new technologies and the power given by the science to the scientists. Moreover, irrational attitudes towards science are often prompted by a broad scientific illiteracy. The result is a remarkable gap between the community of scientists and the society at large. The need for science communication, therefore, comes not only from the fact that the public wants to be informed, but also from the fact that it has the right to be so. In a “risk society”, as defined by the sociologist Ulrich Beck, in which the image of science as a certain and reliable knowledge is hopelessly out-dated, the citizens can no longer accept top-down choices – albeit supported by the opinions of recognized experts – without being properly informed and involved2.

Promoting math interest in Europe is becoming a crucial need, not only for the subject (e.g. to call more resources and funding by the governments and the European Commission), but more deeply for our society and culture. A basic knowledge in mathematics is required to understand and face current political and social challenges, and an appraisal of mathematical culture is an absolute precondition for laying the foundations of modern and complete European citizens. “Mathematics

is the key enabling skill for technological innovation and more sustainable development. Mathematics is the key for a deeper understanding of reality. However, even nowadays, this centrality of mathematics to modern life is not well recognized by laymen or our governaments, and it is a hard but fundamental task to try to change this common misperception”3.

1

The Standard Eurobarometer was established in 1974. Each survey consists of approximately 1000 face-to-face interviews per country. Reports are published twice yearly. Eurobarometer surveys monitor the evolution of public opinion in all 28 EU Member States. The aim is to assess EU citizens’ awareness of and support for the European Union's activities. Tracing public opinion trends helps the preparation of policy, decision-making, and the evaluation of the EU's work.

2_{AAVV (2010), Science and Technology Report. Special Eurobarometer 340 / Wave 73.1 – TNS Opinion & Social, p.}

8-24

(11)

2

With few exceptions, as South Korea and Finland, international surveys are almost unanimous in denouncing the absence of scientific culture of the population, even in the most advanced countries. The European concern about young people lack of preparation in scientific disciplines, mainly in mathematics, has become matter of public debate. Ignored in the past, international surveys results on students qualification, such as those in PISA4, are emphasized in the newspapers. Add to that the fact that sources of friction between science and society keep piling up because of the consequences of the introduction of new technologies, the choices which we are compelled by new opportunities offered, and the impact of new findings on belief and values on which our identity, culture and ways of thinking rely on.

In recent times, communicating mathematics is faced with a substrate of pervasive simplification and a sort of demonization of formal speeches, where almost anything is translated into poor and inappropriate terms. There’s no perception that science is part of our lives and the feeling in respect of mathematics is becoming more and more negative. Moreover, many educated people think that they are unable to understand it, even broadly speaking, and it is a source of pride to them. Internal communication among mathematicians and scientists follows rules different from communication targeted at the general public. And today we can no longer afford to ignore how do people feel about science and mathematics outside our department or laboratory doors.

Researchers are often neither trained to communicate their findings and results to a non-specialized audience, nor they are interested in transmitting the beauty and importance of their field to the general public. This depends on many factors: the most important being probably the fact that so far dissemination and outreach have never played a relevant role in building academic career (at least in Italy)5. On the other hand, in a world in which science is increasingly specialized, journalists are often unable to understand, hence to communicate, the specific results of the various disciplines. We experience more and more the need for the “connection disseminators” which George Thomson6 already imagined in his book The Foreseeable Future (1957). In his words:

“Dissemination should be greatly extended. It is not easy to do, and those who can do it successfully fully deserve a high place in the estimation as scientific researchers”. Connection

disseminators means new mass communicators with a strong technical expertise, but also with marked critical skills: persons who are able not only to understand the technical contents of a scientific or mathematical result, but also to frame it in the right historical, philosophical, ethical and social context.

For most of the 20th Century, mathematicians were free to pursue their subject essentially independently of the rest of human society and culture. In his celebrated book A Mathematician’s

Apology7, G.H. Hardy wrote: “It is a melancholy experience for a professional mathematician to

find himself writing about mathematics”. In Hardy’s view, writing about existing mathematics

4_{Program for International Student Assessment (PISA) is an international survey brought by Organization for}

Economic Co-operation and Development (OECD).

5

Something is changing after, in the last two years, the so called "third mission" has been introduced and evaluated in Italian Universities following a disposition of the Italian Ministery of Univeristy and Research.

6_{George Paget Thomson (1892-1975) was a well-known british physicist who proved the electron wave-particle duality}

together but regardless of the american physicist Clinton Joseph Davisson. Because of that discovery, they were awarded with the Nobel Prize in 1937.

7

(12)

3

paled into insignificance when compared to creating new mathematics. In many ways he was, and still is, right, but the two activities are not mutually exclusive. Moreover, as the 20th Century has given way to 21st, it has become increasingly vital for mathematicians to take steps to increase public awareness of their motives, activities, concerns and contributions. Such awareness has direct benefits for the mathematical enterprise, even if that is viewed entirely selfishly. Fortunately, many mathematicians are now convinced that writing about mathematics is at least as valuable as writing mathematics. To paraphrase Felix Klein, it would be pointless for mathematicians to invent new theorems unless the public gets to hear of them. Not the details, of course, but the general nature of the enterprise. In particular, that new mathematics is constantly being created, and what it is used for. The target of communication is not to transform the whole public of non experts in mathematicians. However, it’s a duty to strive to understand the intellectual and collective work and, more generally, the sense of the scientific enterprise that is the basis of the modern conception of the world. In 1994, the American astronomer Carl Sagan received the Public Welfare Medal by the National Academy of Science. With this award, he denied two strong misconceptions floating around among scientists who used to communicate with the general public: the idea that scientists doing it deprive valuable time to the research and the idea that a researcher is not able to be understood from others, as if his mental universe is so far from that of a layman to be in need of a “translator”.

Fortunately, in the last years these ideas are slowly disappearing. On one hand, here in Europe, we are realizing that it is important to encourage, also from the economic, political and career viewpoint, the communication activity of those researchers who are able to do it. As an evidence of this trend, just think about Cédric Villani, winner of the Fields Medal in 2010 and currently engaged solely in communication activities, providing with his work great benefits for the whole French mathematical community. Moreover, it is enough to observe the focus on dissemination activities within the Sixth Framework Program (FP6) and, more recently, within the calls of the Horizon 2020. On the other hand, we witness the proliferation of courses targeted to train science journalists and communicators able to dialogue with the scientific community and correctly report to the general audience. Therefore, science communication becomes a field of advanced research, which requires strong innovation and development.

The European institutions themselves, from the Royal Society to the Académie des Sciences, from the Max Planck Gesellschaft up to the recent introduction of the so called Third Mission for the Italian Universities, are inviting their members to communicate their research findings and raise the public awareness of mathematics and sciences in general. What was before seen as a waste of time is now outlined as a must. That requires to step outside the boundaries, also human, of specialisation and share their passions with others. Whatever purposes will be behind the decision for communicating, talking about science and mathematics, in addition to spreading knowledge, helps to raise awareness of the value of scientific and mathematical thinking, and of a reasonable and positive approach to the problems, even with those that have nothing to do with science. Furthermore, the effort of communicating mathematics sheds light on the process, clarifies ideas and unlocks complex stages. Paradoxically, science communication with the public can also help to

(13)

4

inform other researchers of their activities and go beyond the barriers among different areas and fields8.

Getting acquainted with science communication techniques may be useful in teaching. Although students have a specific reason to study and be applied, the ability to engage them and the strategies to keep the audience riveted are precious tools for every teacher. The school is the first place where we can make mathematics more attractive and interesting. It is essential to improve the public image of mathematics in our everyday lives by creating an appropriate language to put young people in touch with our scientific experience.

In the post-academic science era, the communication between the scientist and the public has become fundamental. Communication system gives a strong dynamic to the scientific process and contributes to science evolution. However, the system itself is evolving and changing across time. There are several public figures inside this system which contribute to take relevant decisions on the development of science in different forms, at different levels and in an extremely dynamic way9. These public figures don’t have the sole referent in the scientist, but talk to each other. The emergent structure looks like an archipelago where all the islands are interconnected with bridges on which they can convey important information flows in both directions. In this archipelago there is no central control, but a number of centers with different decision-making power on the overall governance of the “city”. Nor there is an outskirts, but a bit more peripherical set of islands. In addition, every bridge is unique because it connects different points of different islands in different ways. Therefore, we need to have both an analytical and a synthetic view of the archipelago, because the structure of science communication is a complex evolutionary phenomena with unexpected, unpredictable and emerging behaviours.

In this context, the science of complexity plays a central role, catering a unitary overview to the world and allowing us a holistic understanding of reality. The complexity approach takes into account the correlations among the different levels of reality of the science communication system and the circularity established among its components. Science communication will play a crucial role in the growth of future society. It’s important to desing and developed actual communication strategies, targeted to the background and needs of the audience: from policy makers to potential industrial partners, from youth and school teachers to the general public. To achieve such an ambitious goal, a good deal could be to form an interdisciplinary team with all the skills and competences for a correct and sound scientific communication. It will feed the exchange of experiences and knowledge among research fields traditionally distant, comparing different methods and making use of tools and methods from non-linear dynamics and chaos theory.

The scientific communication can really support a unifying and interdisciplinary vision of science, overcoming any division into specific branches and specialization, according to the opinion that Stanislaw Ulam attributes to Stefan Banach in his Adventures of a mathematician10. Banach’s vision deals with mathematics, but it can be easily extended to a wider setting, substituting below “mathematician” with “scientist”. It describes a clever mathematician as one able to discover

8_{Carrada G. (2005), Comunicare la scienza. Kit di sopravvivenza per ricercatori. I Quaderni del MdS.} 9

Greco P. (2004), Il modello Venezia. La comunicazione nell’era post accademica della scienza. In: Pitrelli N., Sturloni G. (eds), La comunicazione della scienza. Atti del I e II convegno nazionale. Roma-Milano, Zadig, p. 11-38.

(14)

5

analogies between theories, while a genius is who’s able to see analogies even between analogies, so as to unveil the most intimate and deepest roots and connections of science. A vision that shows how the complexity language, the emergent phenomena, and, in general, the non-linearity, could be usefully described with appropriate mathematical and communication tools recently developed in interdisciplinarity fields like cybernatics in the fifties, system dynamics in the sixties, financial market analysis in the eighties, up to the study of complex networks.

How could we make this happen? Finding new strategies and tools to communicate in a language accessible to the public the methods and the results of the mathematics within the complexity. Dino Buzzati (1906-1972), an italian writer and journalist, wrote this in a letter to the italian poet and essayst Leonardo Sinisgalli (1908-1981): “The normal rule of dissemination is that the scientist

falls. Here is the reader that rises.”; the scientist have to go down, but not too much, then asking a

little effort to the reader/listener without exaggeration. The concepts, methods and results of mathematical complexity, and of mathematics in general, must be communicated in a simple, but not distorted, way without lowering the level and avoiding too spectacular tones. Even Albert Einstein told that most scientific tests intended for non-specialists try to impress on the reader rather than explain in clear and understandable terms the aims and the basic methods.

On the one hand, the new information and communication technologies (ICT) are key tools valid for a wide-ranging dissemination and communication of science. The major social networks like Facebook and Twitter, along with the blogs, are widely used to communicate new findings and advances of science, allowing you to keep in touch with a huge number of “followers”. Massive Open Online Courses (MOOC) and Moodel-based platforms are opening new technological frontiers for teaching. The static nature of web sites has been almost entirely supplanted by the use of dynamic new platforms, as well as is very common, for example, the use of YouTube channels with videos, interviews, seminars and thematic lessons to achieve the public in a more widespread and effective way. On the other hand, the use of non-standard places and unconventional approaches for science dissemination and outreach allow to present science under different reading levels according to the culture and the interests of the different possible participants, becoming mine of ideas for thoughts and new insights.

Everything comes from the idea of giving back to mathematics those moments and situations from which it is artificially separated when encoded in an article or in a manual, enlightening the creative and dynamic aspects that distinguishes it. The aims are, first, removing the erroneous caricature of abstruse, barren, useless and far from the meaning of existence discipline, and then trying to reveal how mathematics is the very essence of the reasoning inherent in each of us and of how the things work in the world around us. “It’s worth making people aware that new mathematics

is constantly being created. This objective is more important than explaining what that new mathematics consists of, and it is more important than explaining what mathematics actually is. Only when people recognise that mathematicians are doing something do they start to get interested in what they are doing. Only when they’ve seen examples of what mathematicians are doing do they start to wonder what mathematics is”11.

11_{Stewart I. (2006), Mathematics, the Media and the Public. Proceedings of the International Congress of}

(15)

6

However, the role of mathematics in maintaining society is seldom appreciated, mostly because it takes place behind the scenes. Although the role of mathematical sciences in civilization has been of central importance for centuries, the current trend to a global economy and a knowledge society has made information and innovation technologies increasingly dependent on scientific research, whose results and techniques are underpinned and driven by mathematics. “It is a common interest of the

entire mathematical community to outreach activities to make society and industry aware that mathematics is the common denominator of much that goes on in everyday life, activating the many sectors of society that can benefit from mathematics. Indeed, promoting such awareness will bring resources to all mathematicians”12. Mathematicians or scientists must invest the necessary time and work in communicating mathematics, and the mathematical community should have the energy to make the outreach effort. A change of attitude of mathematicians towards public awareness of their discipline is vital. It is necessary to enhance the internal level of consciousness in the mathematical community because improving communication could be very useful for the future research. The main focus of a global policy to promote mathematics among the public should concern strategies and ideas to implement in order to have a deep impact on society as a whole. We have to reach a wider audience to show the real value of present and past mathematical results. We have to be more appealing always maintaining a sufficient standard of accuracy, avoiding excesses and cliches, and creating astonishing situations with the right mixture between science and entertainment, that is ultimately the heart of the communication strategy.

In an overall sense, mathematical thinking is, after speech, the most important human faculty. It was this skill especially that helped the human species in the struggle for survival and improved the competitive abilities of societies. I believe that mathematical thinking has a special place in evolution. By mathematical thinking I mean analytic and logical thinking in a very broad sense, which is certainly not independent of the ability to speak. Of course, the development of mathematics as a science is a cultural achievement but, in contrast to languages, it developed in a similar way in different societies. We can face the fact that the importance of mathematics for mankind has grown continuously over the centuries, regardless of the cultural and social systems. No modern science is possible without mathematics and societies with highly developed sciences are in general more competitive than others. Attaching this value to mathematics, one must conclude that society has the fundamental right to demand an appropriate explanation of mathematics. And it is the duty of mathematicians to face this responsibility.

Next to a mathematical vision is increasingly necessary a “philosophical” vision, in accordance with the original etymology of this word: philosophy as love to wisdom, and consequently to science, again meant in a global sense, intrinsically related to the real world and its cultural and civil progress. It’s also equally important an “historical” vision of the science. Science communication can’t forget the way in which revolutions, ideas and scientific methods are born, as much as the scientists who developed them, so as to be seen as men of their time, culture and society.

In this perspective, fruitful collaborations are possible if each person involved is willing to contaminate their specialization through learning the language and the specificity of the others. These contaminations are not synonymous with superficiality, dispersion and amateurism, but opportunities to create special connections, collaborations and synergies that lead to deeper and

12

(16)

7

original visions of what are generally obtained in an internal logic to the individual disciplines. There could be risks, but I agree with Leonardo Sinisgalli when states that “it needed a symbiosis

between intellect and instinct, reason and passion, real and imaginary; it was urgent to try a mingling, a graft, even if it means sacrificing the purity”.

Within this landscape arises my research project whose main target is to find an attractive and effective way to communicate complexity theory to the general public and at the same time to use complexity theory to communicate science in general. Science of complexity is interested in the complex and unpredictable links among various systems among which the physical and social ones, and allows an holistic, less pretentious and more careful understanding of reality. It gives us a new way of looking at the system as a whole and a clear insight about its organization taking into account the relations among different levels of reality and the circularity that happens between the system and the environment. So, the science of complex systems is both multidisciplinary and interdisciplinary. It feeds off knowledge and experience exchange among research fields traditionally far apart, and comparison among different methods. Along these lines, a reference point is, for example, Santa Fe Institute, born in the 80s in New Mexico (USA) as a research center where physicists, mathematicians, computer scientists, biologists, sociologists, economists and others study the diversity of the complex phenomena searching for common origin and language. The word “complexity” is too vague and generic. It has to do with interaction, interdisciplinarity, emergent behaviors and nonlinearity, and all too often is open to misunderstanding among common people. Complexity refers to interweaving of the fabric. While being constituted by different parts, it possesses features that the individual parts haven’t got and can be explained only to a limited extent undoing it. Hence, the simple is no longer the foundation of all the things, but just an articulation among different complexities. Consequently, the complexity of the world requires thinking able to face and engage with it. In order to understand complex phenomena we have to accept that between causes and effect could be a circular relationship different from the basic idea classical way of thinking. We need a circularity in thinking that increases our ability to understand, without falling back on a vicious cycle. We can apply this kind of vision in various areas from social studies to economics, from biology to physics, from meteorology to functioning of the immune system, from neuroscience to teaching: all systems where dynamic order and organization emerge from an underlying simplicity across a self-organization process. Communication itself is a complex science.

To understand and look at the bigger picture of complexity we have to accept a counterintuitive and nonlinear causality which can often feel like unexpected and astonishing. We have to focus our attention on self-organization process which makes possible that highly organized behaviors could arise from relationships circularities in the absence of a project. This can include the language. In the process of interaction with the text by which we understand its meaning, we understand the phrase starting with the meaning of the words. But, at the same time, the meaning of the words sets out based on what emerges in terms of global meaning of the phrase13. This kind of self-organization could seem paradoxical: the system as a whole is more than the sum of its parts, precisely because self-organization emerges, but is also less than the sum of its parts, because it carries out just one of the possible organizations.

13

(17)

8

Before I face the problem of how to communicate complexity, and how using complexity ideas to communicate mathematics, I have to deal with the complexity embodied in communicating mathematics. This has forced me to be familiar with the past and present masters of science and mathematics communication starting from Galielo Galilei via Michael Faraday until Ian Stewart . I had to learn how they did it in the past and do it nowadays. I wanted to understand why they started doing that and how communicating mathematics has changed over the years. I needed to know better approaches, methods and strategies they use for an effective communication. I wanted to analyze in detail the difficulties they face in communicating mathematics, the objectives they set out, the styles they use with different audience, what’s worth communicating and the tools of the trade.

Early on, I realized to have a huge amount of literature on science communication and communication in general, but short of material on mathematics communication. So, I wondered how I can remedy this and the answer was a journey. That’s the second step of my research project. I’ve been on a journey of knowledge, discovery and first-hand experience around Europe to find out scientific and organizational models that have led and are leading to special achievements in communicating mathematics. A direct result has been my personal meetings with some of the greatest experts in the field like Chris Budd, Alex Bellos, Andrew Jeffrey, Simon Singh, Kristof Fenyvesi, Andreas Matt, Eduardo Sáenz de Cabezon, Rogerio Martins, Cedric Villani and many others. Visiting periods, participation in conferences and events, direct cooperation and interviews have been key moments in my research path. The report of this journey has also become a series of articles entitled “Communicating mathematics in Europe” in the quarterly magazine Lettera

Matematica14 organized by Pristem Research Center and edited by Springer both in the italian and the international edition.

During this journey, I’ve also developed projects and events focused on communicating mathematics to the general public, presented workshops for students and teachers, written a book for kids from 9-years-old and up based on an innovative approach to mathematics, and started creating a show on chaos and complexity which involves music, dance and visual graphics.

Chapter 2 collects the first three articles in the series “Communicating mathematics in Europe” for the international Springer journal Lettera Matematica Pristem.

Chapter 3 provides an in-depth review of science and mathematics communication literature. In the first part, I start trying to answer questions like “Why to communicate?”, “Who have to communicate?”, “How to communicate?” and “Who is the public?”. I reflect on the differences between the “deficit” model and “dialogue” model in science communication and how from them we have arrived to a three-pronged approach consisting of communication, consultation and participation. Then, I quickly retrace the historical evolution of science popularization to the present day. In the second part, I move from science communication to mathematics communication

14_{Lettera Matematica is a quarterly journal, that has the objective of discussing mathematics and the world that}

revolves around it, thereby embracing other fields of knowledge and engaging other scientific communities. The journal addresses topics related to mathematical research but also aims to discuss and reflect on society and its relationships to scientific culture, underlining the contribution that the mathematician – like all other intellectuals – can and must make to the growth and well-balanced development of society. It also provides common ground for those mathematicians who use their chosen discipline as a bridge to other worlds rather than working in isolation.

(18)

9

highlighting the main obstacles and challenges we have to face with, in particular those of language and rigour, and how we can reinforce the message we’d like to convey.

Public Engagement and Outreach are the key words in Chapter 4. After a brief introduction of the close link among engagement, outreach activities and communication, I analyse thoroughly three live or face-to-face communication events like science festival, math busking and science cafes. I start describing my first-hand experience in Bath Taps Into Science festival and Birmingham Big Bang Fair during my visiting period at the University of Bath and what I learned from that. Then, I present in detail some engagement and outreach activities I’ve designed, set up and/or taken part in: FermHAmente Science Festival, VereMath Street, Scienza in Vacanza and a series of Science Cafes. The last three have been carried out together with the research group Unicam Science Outreach in which I’m included since July 2015, and of which I outline the main goals. There is also a section dedicated to a proposal for a maths/science communication course drawn up during the Imaginary Conference held in Berlin in July 2016.

In Chapter 5, I tackle the issue of how communication can improve teaching. At the beginning, I explore the benefits teachers could obtain by using popularization techniques into a teaching/learning environment, how storytelling can be an effective tool to communicate and teach mathematics, and how laboratorial activities can enhance students perception about mathematics improving their reasoning skills, mathematical thinking and analytical capabilities. Then, I present the book “Il tranello e la soluzione matematica” by Andrea Capozucca and Barbara Cerquetti and the whole project behind it, and a laboratorial activity project involving mathematics and dance. In particular, I underline the idea of the book as an innovative tool for teaching mathematics in an engaging, interactive and interdisciplinary way, and the importance of a “whole body” learning approach to mathematics as I first-hand experienced with Erik Stern and his math-dance research group.

Chapter 6 provides an overview of the FOTCAB project, an interdisciplinary show/exhibition to communicate complexity and chaos theory to the public. After a description of the overall structure of the project, choices I do and methods I use, I go into detail as regards its main aims, its implementation and development. Then, I set out the project outline and present what has been carried out so far. The project is still work in progress.

Finally, in Chapter 7 I give a short summary of the whole journey reasoning on the evidence I have accumulated, a quick overview of the limitations I experienced and suggestions for future implementations and developments of the undertaken lines of research and projects.

(19)

Chapter 2 Articles in Lettera Matematica Pristem

This chapter collects, in chronological order, the first three articles of the series “Communicating mathematics in Europe” that I have written for Lettera Matematica edited by Springer and Centro P.RI.ST.EM Bocconi University of Milan. Each article is structured around an interview with an European master maths communicator, and deepens specific themes related to mathematics communication. Guests of these three episodes are Chris Budd, Alex Bellos and Andrew Jeffrey. All the articles are translated by Daniele A. Gewurz.

2.1 Article 1: Chris Budd

Lettera Matematica n.98 – ottobre 2016

Lettera Matematica International Edition, Springer-Verlag © Centro P.RI.ST.EM, Università Commerciale Luigi Bocconi 2016

DOI 10.1007/s40329-016-0147-z

Abstract. This article is the first in a series on the communication of mathematics in Europe. In this

first instalment Andrea Capozucca visits with Prof. Christopher Budd, OBE. Some of the topics covered in the interview with Budd are the golden rules for an effective communication, the ways to improve skills and nourish passions, past, present and future projects, Bath Taps into Science, the events of the British Science Week, and much more. The result is a snapshot of the present state of the communication of mathematics, seen through the eyes of one of the leading figures in the field of public engagement and outreach. The author also experienced first-hand the methods and tools used in communicating maths in Britain, leading to a relection on the importance of the communication of science today.

Keywords. Chris Budd – Bath Taps into Science – Popular science – Maths communication -

Outreach – Public engagement – Interdisciplinarity

Communicating mathematics

My doctoral research project is about the communication of mathematics, and especially the construction of new tools, original, interdisciplinary approaches to science outreach, and public

(20)

11

engagement with mathematics, sciences and technology. The first problem in a new project is always the same: where to start? If we want to look beyond the horizon, we have to climb “on the

shoulders of giants” ([7], p. 167). Thus, why not begin with a journey? A journey of knowledge,

discovery and foundations. A tour around Europe to meet the protagonists and the main stages in the field of mathematical communication, to discover and experiment personally ways and methods used by those “giants” to build and improve the tools a good communicator must have in order to be effective and reliable, taking as a model the most advanced results and the most important projects in Europe. I had the same idea as Enrico Betti, Francesco Brioschi and Felice Casorati who, in September 1858, began a journey through France and Germany to meet the most important mathematicians of the time, to “form contacts with the protagonists of the most advanced studies

and ‘photograph’ mindsets, structures and organisations that made these great achievements possible” [6].

The adventure begins

First stop in my journey: the University of Bath, to meet Chris Budd, who has been working for several years in the field of communicating mathematics (Fig. 2.1). He is a professor of mathematics at the Royal Institution of Great Britain, vice-president of the Institute for Mathematics and its Applications (IMA), the founder and director of the Bath Taps into Science festival, as well the recipient, in the last twenty years, of several awards for his work in scientific and mathematical education, including the Order of the British Empire (OBE), bestowed by Queen Elizabeth.

Fig. 2.1 – Prof Chris Budd in his office

And now I have arrived. “I have an appointment with Professor Budd. I am Andrea Capozucca.” At my side sits a blonde girl with a book in her lap. The lift’s doors open, and an unprepossessing man gets out; he wears a symmetrically patterned green wool jumper and has a cup of cofee in his left hand. He is Budd, I immediately recognise him. I am about to get up, but I realise that he is looking at the girl on my right. Without hesitating, as soon as he is out of the lift, he turns left and in a few steps he is in front of her. “Andrea? Welcome to Bath!”, he tells her holding out his hand. She looks up, surprised, and answers, “Er… Actually, I am not Andrea. My name is Helen. I am

sorry.” A chill descends on the entrance hall. Budd is incredulous. Now, having realised the

misunderstanding, I get up and in a moment I am behind him. I tap him on a shoulder saying:

(21)

12

puzzled look I understand he did not expect to see a man, much less one as big as me. Our only contacts, in the last few months, had been by email; this was the first time we met in person. In a moment his initial perplexity turns into a wide smile that breaks the embarrassment. “Andrea? I

have a niece called Andrea. The name deceived me.” Another smile, and he shakes my hand and

shows me the way towards his oice, to plan together my stay there. As soon as we are in the lift, he looks at me and continues, “It’ll be okay. Some arrangements will have to be changed, as you may

imagine, but no problem. It will be 2 weeks full of work and meetings. Are you ready? Welcome to Bath!”

“This is my oice. Settle down wherever you can find room.” Budd’s welcoming voice takes me

back to the here and now. I go in and drop my backpack on the first empty chair. The other ones are around a round table almost completely covered by books, folders, posters and boxes. While Budd reaches his desk to get his laptop, I look around the room, curious. On the wall on my right is a blackboard chock-full of equations and notes about some mesh methods used to improve the accuracy of weather forecasting and climate studies; on the opposite wall, a coat rack keeps company with a second bookshelf, propped against which stays a curious green trolley case in which some mathematical puzzles can be glimpsed. But one thing in particular catches my attention: a wonderful cartoon in which I recognise Ian Stewart, Marcus Du Sautoy and other giants of the communication of mathematics (Fig. 2.2). “Call me Chris”, he says passing by me and noticing my interest in the cartoon. “Can you recognise them? They are the champions of popular

mathematics in the United Kingdom. In the foreground, Zeeman, Stewart and Du Sautoy, and behind them all the other ones. A beautiful cartoon we were given some years ago, in 2010, at the end of a IMA conference about public engagement, with all of them, and yours truly as one of the organisers”, Chris remarks. “And how come you are not in the cartoon, Chris?”, I ask, intrigued. “Because I got one all for myself!”, he replies with a smile and points at another cartoon at a short

distance: Chris in a bathtub with a double pendulum and some butterlies luttering about his head (hinting at the chaos theory, one of his research areas) (Fig. 2.3). So I understand my journey could not have started in a better place.

Fig. 2.2 – The cartoon with the British “champions” of the communication of mathematics

(22)

13

Fig. 2.3 – Prof Budd’s cartoon

His calm but engaging style, the passion and mastery with which he tells what he does and his great ability to listen make everything so much easier. I ask Chris if I may interview him and he answers serenely: “Why, of course, but not right now. We have lots of stuff to do before”. And, with pen and paper, he begins to explain to me in detail the engagements and activities we shall be directly involved in the next 10 days, including taking part in the Big Bang Fair in Birmingham as scientific promoters at the IMA stand, together with the public engagement and maths communication group led by John Meeson, as well as organising and mounting the “Bath Taps into Science” festival in Bath. Afterwards, he says, “That is all, for today. Let’s meet tomorrow at 9, here, in my oice. I’ll be

glad to introduce you to Andrew Ross and the rest of the board of the ‘Bath Taps into Science’ festival, to adjust the last details of the programme”. Andrew Ross is the festival project manager

of “Bath Taps into Science” (Fig. 2.4). The other board members I met are Michelle Smith, Margarida Dolan, Bob Draper and Peter Ford (Fig. 2.5).

(23)

14

Fig. 2.5 – Margarida Dolan, who teaches science communication and public engagement to undergraduates and graduates, with one of her student

While going back to my lodgings, I think about the delayed interview and feel like one who goes to a lifeguard to be taught how to swim and, instead of receiving instructions, is directly thrown into water. A method more inductive than deductive taught me that the first rule of a good communicator is being able to put themselves on the line. A good communicator cannot stand still in a single, fixed role, but has to learn how to be flexible, assume multiple roles, and switch from one to another. Thus, immediately to work. Theory may wait, for now. As a consequence, the following days were a valuable and indispensable training ground to refine the essential abilities for an efficient and effective communication of mathematics. They were full and tiring days, but rich in important experiences and different roles to cover. I took part as an observer in a Royal Institution Maths Masterclass, where I learnt that the direct involvement of the audience in hands-on and interactive activities facilitates their understanding of the proposed mathematical notion and improves learning and self-esteem. I had the opportunity to observe and experiment in IMA’s stand in the Big Bang Fair the effectiveness and validity of public engagement as a two-way process that engages attention and listening, with the goal of generating a mutual well-being in the participants. I lived from the inside the organisational dynamics of a science festival and understood the complexity and interconnectedness of its organisation and the perfect coordination of all its components, including the sponsors. I saw the surprised and intrigued faces of people of all ages attending the exhibits of Bath Taps into Science, and their amazement in front of something new, an amazement that is not just an aesthetic feeling, or a momentary curiosity, but the beginning of a process: it kindles the desire to enter into relations with the mathematical (and scientific) world, to know it. Moreover, living alongside Chris I also learnt to understand the greatness of a scientist who gets down from his pedestal to be at the side of his students, to observe them, even help them to tidy up tables and chairs, so transmitting his passion for his work. Lastly, I remember the tiredness, on Saturday afternoon, at the end of the Family Science Fair, the last engagement in our calendar, and my wonder when Chris suggests closing the day with a pint at the historical pub “The Raven” in the

(24)

15

centre of Bath, “I still have an hour before my train to Bristol. Let’s enjoy a well-deserved pint at

the Raven. Every mathematician who passed through Bath has been at least once at the Raven for a beer. So, now it’s your turn” (Fig. 2.6).

Fig. 2.6 – The pub The Raven in Bath

Ten days after our first meeting we are once again back in his oice. Everything is in its place, even the green trolley case that, during the Big Bang Fair, I discovered to be Chris’s “Maths Magic Box”, that is, a collection of games and hands-on activities of increasing difficulty, most of which are based on mathematical principles. They are intended for stands where people will not interact with the promoters for more than 5 minutes, and Budd also uses them to train students who will be personally involved in scientific promotion. Chris gives a course in communication of mathematics whose main goals are to give the students the communication skills required for maths, and soon after that to put these skills in practice in concrete situations, such as science festivals, masterclasses, popular articles, “math busking” and so on. A theoretico-practical course requiring a significant involvement and time investment, during which Chris puts at his students’ disposal all the richness and depth of his experience, including the contents of his green trolley case.

A splendid framed photograph behind him shows him smiling together with his mother, wife and daughter (Fig. 2.7). “It was taken last October at the Windsor Castle. It was an amazing day. I met

lots of incredible people who’d done wonderful things. I was very honoured to meet the Queen herself and she seemed very interested in the Bath Taps into Science fair”, he remarks happily

behind me.

I take the opportunity to ask, “What are the golden rules for a speaker to follow to catch the

listeners’ attention?” “There are really only two rules that I think you should follow”, he replies,

determined. “One is that you should always imagine that you are in the audience. Think what it

would be like for you to be sitting in that audience listening to the person that is giving his talk. So, be completely aware of your audience. Then, the second rule is connect with the audience and be very enthusiastic about what you’re doing, be very positive. Show a lot of interest both in your subject but also in your audience. You should talk to your audience, not at your audience. These are really the only two rules, everything else is a detail. There are diferent styles and all styles would work provided you go by those first two rules”.

(25)

16

Fig. 2.7 – Prof Budd is honoured with OBE at Windsor Castle

(from the left Sue, Prof Budd’s wife, Prof Budd, his daughter Bryony and his mother Jillian)

At this point, it comes naturally to me to ask, “Then, what are the golden rules to communicate

maths?” In a calm voice, he replies, “Maths communication is particularly diicult because lots of mathematics really is beyond the audience. It’s the sort of subject where a lot of background knowledge is often needed to understand something”. A short pause for relection, then he resumes,

conidently, “The two things that I always like to think of are ‘what do I want the audience

understand at the end?’ and ‘how can I get there from what they know?’. And then lead them to that in easy stages trying never to lose them on the way, but also to make them aware of where we’re getting and showing them the importance and relevance of what we’re doing. But I also feel quite strongly that you should never show people mathematics in such a way that you leave apart the audience. If they are coming to hear maths, then give them some maths, but don’t kill them with maths!”, he concludes with a smile and sips from his ever-present cup of cofee. “So, that’s my rule: don’t bring maths down to where the audience is, but bring the audience up to where you want, where you feel they should be”.

Listening these words, I recall what Dino Buzzati wrote in a letter to Leonardo Sinisgalli, then the director of the journal Civiltà delle macchine, that in communication it is the listener that has to rise, in contrast with popularisation, where the scientist goes down. The term “populariser” is still used to denote the scientist who spreads technical or scientiic ideas to the public. Today, however, this notion, where “who knows” pours their knowledge onto “who does not know” in a top-down, one-way relationship in which the learner is completely passive, is outmoded and replaced by a broader notion of communication, where there is a direct involvement on the part of both the communicator and the audience in a two-way flow of information that includes listening, debating and interacting.

Returning to the communication of mathematics, I try to get into more detail: “Is there any aspect

you deem indispensable for an effective communication of maths?”. “As I said earlier”, he replies, “maths communication can be quite hard, because of the nature of our subject. But I think the two things that always we must bear in mind are: maths is a wonderful subject and, if you convey the kind of fun and puzzled and creative side of maths, that’s very important; and, maths is a subject which has many, many applications. What I never want to do is to sell maths just for its

(26)

17

applications or just think of maths as something without applications. You should try to put it in the context of people’s lives to help the communication”.

Chris is an applied mathematician and is known in the mathematical and scientific world for his important contributions in the field of non-linear diferential equations and their applications to industry. He often says, “I am interested in every field to which mathematics is applicable, but we

must not sell maths just for its applications”. From his words a “unitary” mathematics emerges, not

one that is separated, as often occurs, into its pure and applied aspects. Chris goes on, “I’ve never

thought that there has been a separation. If you look at the really great mathematicians like Euler and Gauss, Archimedes and Riemann, people like these saw no separation. They say, ‘It’s just maths’. Yes, there is a separation between purely abstract and applied, but that’s fine because you can tell a good story in that way. A very nice story would be if you look at Fourier who developed the subject of Fourier series as an answer to a problem in conduction of heat. He started with that problem and then from that found the best way for solving it was the Fourier series. And then you can show that the Fourier series lead to a study of waves and the modern study of communication. So, this is where the power of abstraction was so important, because it showed how a mathematical tool, which was used to solve one problem, could then be useful to solve many, many other problems. That’s a great story and Fourier himself was a very interesting guy who was for a while a magistrate in Napoleon’s army in Egypt. This is in itself a story that deserves to be told. A story that enriches and completes the strictly mathematical one”.

Listening to Chris is an ecstatic experience. His ability to speak to audiences of different kinds and absorb the listener are even more impressive in a face-to-face meeting. While I ponder this, my gaze falls on a set of flyers on the table: four brochures of different colours, with different images, all bearing the same title, “Living in a complex world”. “What’s this about?”, I ask. “In 2010 I was

the director of this exhibition, within the Royal Society Summer Exhibition, which was enormously successful. We built four different paths to offer the visitors a hands-on experience about the ways mathematics helps us understand the complexity in the world around us, from weather forecasting and chaos to energy production, from bouncing balls and sand to the behaviour of locks of birds and a crowd in motion. The main goal of the exhibition was to communicate that maths can be used not just to understand complexity, but also to see how to use this knowledge to improve our everyday life. We worked one whole year to create the exhibition! But it was worth it”.

“Chris, do you believe that complexity science can give an answer to the separation between pure and applied mathematics?”, I ask him with interest, since my doctoral program is on complexity

science. “Good question!” he answers with exuberance. “One reason it could be a very good

answer is there’s a lot of complexity science directly related to people’s life. You can talk about crowds for example, or you can talk about the weather, or you can talk about economics. A possible risk with complexity science is that sometimes people make claims which are not really true. So we have to be quite careful to separate the real hard science from what I call the ‘seedy’ science. We have a lot to be careful about!”

We take a short break, and between sips of coffee, Chris replies to some emails and yours truly begins to realise that his time in Bath is almost over. As soon as Chris is again at the table with me, I read him a passage from an article by Umberto Eco [4], in which the great Italian semiologist argued that scientific knowledge should be told through stories. I ask Chris what he thinks about it.

(27)

18

“I suppose it depends on the story”, he replies while checking his watch. “The story I always like to tell is how a mathematical idea can be relevant to someone’s life or how it’s important turned in an application. So, in math way, I think, yes, you can tell a story. However, you’ve got to be a little careful because of course some mathematics just is mathematics. If I’m talking about the formula for π, I feel good enough and it’s all right, in that it doesn’t need to be linked to a story. But one thing I do know is that children or, in fact, adults, like to know about the people behind the mathematics. And I suppose that’s part of a story. So, not just something that you have in a book, but someone like Euler or Galois. Florence Nightingale15 was responsible for some mathematics and you can tell the story about the person. And others that I found very effective”.

In short, storytelling is fine, but with great care. Tales may be interesting, but another problem arises. When we talk about mathematics, we must keep in mind formal rigour: it is difficult to even imagine a non-rigorous maths, and it is quite legitimate to raise the doubt whether it is possible to communicate maths omitting rigour. On the other hand, non-mathematicians may by scared by even a single formula in a text, just as a sentence including strictly technical terms completely excludes those who don’t know the meaning of the terms. The journalist and science writer Pietro Greco himself proposes, in this regard, an uncertainty principle for science communication that says “I

cannot express a scientific notion, simultaneously, with both a maximum of communicability and a maximum of rigour” ([5], p. 19). This holds especially for mathematics. Chris nods and points out

that this idea dates back to Michael Faraday, the great 19th-century communicator. “He had exactly

the same vision as Mr Greco”, Chris says. After telling me how the Royal Institution’s Christmas

Lectures, started in 1825 by Michael Faraday who gave several of them, were the first attempt to communicate science to the general public, he adds, “Obviously if I went in front of an audience

and talk with full rigour about mathematics, I would lose everybody almost immediately. So, you don’t do that, you have to be reasonable. It’s actually the same with the undergraduate teaching. If you go with full rigour to an undergraduate, he would not understand. So, my plan with undergraduate teaching is always to give the basic ideas and then say to the students where they can look this up, then trying to get more details. I think the same holds for communication. If you get the basic enthusiasm, people can always follow you up if they need to. But you have to make compromises”. As soon as Chris stops, I remind him about Mathscot!, the yellow character who

sponsored the “MathsCounts” programme and who wandered about the stands in Birmingham to let himself be photographed with the visitors. And I tell Chris, “Mathscot! looks like a perfect

compromise!” We both burst into laughter, then Chris remarks seriously, “That is an example of how not to communicate maths!”

I take the opportunity to thank him again for the wonderful experience I had in the IMA stand at the Big Bang Fair in Birmingham and we end by talking about his “creature”, the Bath Taps into Science festival. I ask him when and how the idea of the festival was born, getting Chris started.

“Bath Taps started in year 2000. The reason we started then was we wanted to mark the new millennium and we thought this ‘a great tangible sign would be to have a science fair’. So, I started quite a small fair that now has become quite a big fair. How do we choose the topics? We like to

15

Florence Nightingale showed that statistics could be used in an effective way as a basis to significantly change the social practices of the time [2].